Claude Cracks Knuth's Hamiltonian-Cycle Conjecture as Apple Debuts $599 MacBook Neo

Legendary mathematician Donald Knuth revealed that Claude Opus 4.6 cracked his long-standing Hamiltonian-cycle conjecture for all odd sizes, calling it "a joy." A Hamiltonian cycle is a path through a graph that visits every point exactly once and returns to the start.

Anthropic's models also dominated BullshitBench v2, where they excelled at challenging nonsensical prompts rather than confidently answering them, while competitors flatlined.

OpenAI is reportedly countering with scale: GPT-5.4 will bring a million-token context window and "extreme" reasoning.

Stanford's Speculative Speculative Decoding achieved 5x faster inference by parallelizing drafting and verification. This technique has the model generate quick draft responses and verify them in parallel rather than sequentially.

Q Labs' NanoGPT Slowrun, a new benchmark for compute-abundant, data-scarce training regimes, saw its top entry achieve 5.5x data efficiency.

OpenAI brought Codex to Windows with multi-agent coordination and native sandboxing, is prepping its IPO, and expects to double its consumer revenue to $17B using ads.

Former OpenAI research chief Bob McGrew began raising $70M for Arda, to train AI on factory floor footage to automate manufacturing.

Unity's CEO revealed an AI beta that prompts full casual games into existence with natural language alone.

Google's NotebookLM introduced cinematic video overviews, and a new open-source Workspace CLI with 40+ agent skills for Drive, Gmail, and Calendar.

A Claude agent grew Trophy tomatoes from seed to fruit over 100 days, checking sensors every two hours, pollinating flowers, and surviving a critical system failure.

A wrongful death lawsuit alleges Gemini sent a man on missions to find it an android body and set a suicide countdown.

Nearby Glasses launched to alert users when smart glasses are watching.

Apple's MacBook Neo debuted at $599, the cheapest Apple laptop ever, a fanless A18 Pro with 16 hours of battery life.

xAI committed 1.2 GW of power to its AI data centers, expanding the world's largest Megapack installation.

Broadcom posted record Q1 revenue of $19.3B with AI revenue doubling to $8.4B, projecting AI chip revenue alone exceeding $100B by 2027.

The Arc Institute's Evo 2 model landed in Nature with the first AI-designed bacteriophages. Bacteriophages are viruses that infect bacteria, and 16 of its 285 generated designs selectively killed target bacteria.

A Nature paper introduced GEMINI, a genetically encoded protein assembly that grows inside living cells and records their signaling history as tree-ring-like fluorescent patterns.

A PNAS study found humans 40,000 years ago carved geometric signs on figurines rivaling early protocuneiform in complexity. Protocuneiform was an early writing system from ancient Mesopotamia.

Barclays estimated the market spanning humanoids, AVs, and industrial automation could hit $1.4 trillion by 2035.

Carbon Robotics unveiled a Large Plant Model of 150 million labeled plants, letting farmers laser-weed any crop in minutes.

NVIDIA posted a job for an Orbital Datacenter Architect.

Anders Sandberg calculated that at 12% annual data center growth, a full Dyson Swarm would require 320 years.

NASA FORCE launched to recruit elite engineers, and Artemis 2 targeted April for its crewed lunar flyby.

Jensen Huang called Nvidia's investments in OpenAI and Anthropic likely its last due to OpenAI's imminent IPO.

The Washington Post reported Claude remained central to US strikes in Iran via the Maven platform despite a White House ban.

China announced 7% more military spending and a five-year push into quantum, fusion, BCIs, and 6G.

The Pentagon sought 13 critical minerals the day before Iran strikes and began evaluating $35,500 Ukrainian drone interceptors over $13.5M Patriots.

A US sub sank the Iranian IRIS Dena, the first submarine combat kill since WWII.

Jim O'Neill, Thiel Fellowship co-founder, was nominated to lead the NSF.

Michigan sued Kalshi as Polymarket countersued, with prediction markets becoming the latest jurisdictional flashpoint.

Over 40 organizations signed a declaration to prohibit superintelligence without scientific consensus.

Naval Ravikant observed the only career divide left is "good with AI" versus not.